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Research Article | Open Access

Note on a class of time-delay virus models with virus-to-cell infection, cell-to-cell transmission, CTL and antibody immune responses

Yan Li1, Rui Zhu2, Xiaoqun Li3( ), Xianshan Yang2, Yong Li2, Ruixia Yuan4( )
School of Information Engineering, Wuhan Huaxia Institute of Technology, Wuhan 430223, China
School of Information and Mathematics, Yangtze University, Jingzhou 434023, China
Research School of Finance, Actuarial Studies and Statistics, The Australian National University, Canberra 2601, Australia
College of Business and Economics, Shanghai Business School, Shanghai 201400, China
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Abstract

This paper investigates the coexistence of equilibria and local and global asymptotic stability of a class of time-delay virus models involving virus-to-cell infection, cell-to-cell transmission, Cytotoxic T Lymphocytes (CTL), and antibody immune responses. These models typically exhibit five equilibria; however, the existing literature lacks comprehensive studies on the uniqueness and coexistence of these equilibria. Our study fills the gaps and rectifies the shortcomings or lack of rigor in certain prior research.

Keywords

virus-to-cell infectioncell-to-cell transmissionCTL and antibody immune responsesco-existencestability analysis
CLC number: 34D23, 92B05

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AIMS Mathematics
Volume 10 Issue 11,
November 2025
Pages 26446-26458
DOI: 10.3934/math.20251162

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Li Y, Zhu R, Li X, et al. Note on a class of time-delay virus models with virus-to-cell infection, cell-to-cell transmission, CTL and antibody immune responses. AIMS Mathematics, 2025, 10(11): 26446-26458. https://doi.org/10.3934/math.20251162

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Received: 03 September 2025
Revised: 03 November 2025
Accepted: 05 November 2025
Published: 17 November 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)